Hypergeometric series solutions of linear operator equations

DOI10.1016/j.amc.2009.11.013zbMath1183.33011OpenAlexW2054150283MaRDI QIDQ846494

Yan-Ping Mu, Qing-Hu Hou

Publication date: 9 February 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.11.013

zbMATH Keywords

orthogonal polynomialshypergeometric seriesthree term recurrence relationsdifferential/difference equations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Generalized hypergeometric series, ({}_pF_q) (33C20)

Uses Software

• SumTools
• retode

Cites Work

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• Rational normal forms and minimal decompositions of hypergeometric terms
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Representations of orthogonal polynomials
• Recurrence equations and their classical orthogonal polynomial solutions
• Algorithms for \(m\)-fold hypergeometric summation
• Special formal series solutions of linear operator equations
• On difference equations for orthogonal polynomials on nonuniform lattices¹
• A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it